In this paper, the first-order non-negative integer-valued autoregressive process with Poisson-transmuted exponential innovations is introduced. Three estimation methods, namely, the conditional maximum likelihood, conditional least squares and Yule-Walker estimation methods are discussed to estimate the unknown parameters of the proposed process. Additionally, the simulation study is presented to

In this paper, by considering two multi-state semi-coherent systems sharing some components, we define the multi-state joint signature. Then, some properties of this multi-state joint signature are discussed in detail, and some preservation results are established in terms of stochastic ordering. A south-east shift order for comparing the multi-state joint signature matrices is then discussed. Finally

This paper considers a continuous-time quasi birth-death (qbd) process, which informally can be seen as a birth-death process of which the parameters are modulated by an external continuous-time Markov chain. The aim is to numerically approximate the time-dependent distribution of the resulting bivariate Markov process in an accurate and efficient way. An approach based on the Erlangization principle

A new robust class of multivariate skew distributions is introduced. Practical aspects such as parameter estimation method of the proposed class are discussed, we show that the proposed class can be fitted under a reasonable time frame. Our study shows that the class of distributions is capable to model multivariate skewness structure and does not suffer from the curse of dimensionality as heavily

Traditionally, in reliability acceptance sampling plans, the decision to accept or reject a lot is made by performing the life tests of items. However, when the item’s deterioration is described by a degradation process, it can be made based on the observed deterioration levels of the items obtained from degradation tests. In this paper, two acceptance sampling plans are developed, based on the observation

One of the widely discussed in the literature and relevant in practice shock models is the delta-shock model that is described by the constant time of a system’s recovery after a shock. However, in practice, as time progresses and due to deterioration of a system, this recovery time is gradually increasing. This important phenomenon was not discussed in the literature so far. Therefore, in this paper

In this manuscript we consider the dual risk model with financial application, where the random gains occur under a renewal process. We particularly work the Erlang(n) case for common distribution of the inter-arrival times, from there it is easy to understand that our method or procedures can be generalised to other cases under the matrix-exponential family case. We work several and different problems

This paper exploits the representation of the conditional mean risk sharing allocations in terms of size-biased transforms to derive effective approximations within insurance pools of limited size. Precisely, the probability density functions involved in this representation are expanded with respect to the Gamma density and its associated Laguerre orthonormal polynomials, or with respect to the Normal

The Feynman-Kac formula provides a way to understand solutions to elliptic partial differential equations in terms of expectations of continuous time Markov processes. This connection allows for the creation of numerical schemes for solutions based on samples of these Markov processes which have advantages over traditional numerical methods in some cases. However, naïve numerical implementations suffer

In this paper, we are interested in the dependence between lifetimes based on a joint survival model. This model is built using the bivariate Sarmanov distribution with Phase-Type marginal distributions. Capitalizing on these two classes of distributions’ mathematical properties, we drive some useful closed-form expressions of distributions and quantities of interest in the context of multiple-life

Hawkes processes have been widely studied, but their many probability properties are still difficult to obtain, including their moments. In the paper, we shall give the moments for two classes of linear Hawkes processes with Gamma decay kernel and compound Gamma decay kernel functions by employing the method proposed by Cui et al. (2020), and the relationship between our results and those obtained

In this letter, we test a scalar stochastic nonlinear equation used to portray the growth of a population with Allee effects. We first testify that there is a unique dynamical bifurcation point Λ to the equation, and the sign of Λ determines the dynamical properties of the equation: if Λ is negative, then the equation has a unique invariant measure — the Dirac measure concentrated at zero; if Λ is

Multiple linear regression model based on normally distributed and uncorrelated errors is a popular statistical tool with application in various fields. But these assumptions of normality and no serial correlation are hardly met in real life. Hence, this study considers the linear regression time series model for series with outliers and autocorrelated errors. These autocorrelated errors are represented

In this note, we derive upper bounds on Kendall’s tau and Spearman’s rho for multivariate zero-inflated continuous variables often encountered in insurance. A lower bound for Spearman’s rho is also established in the bivariate case. These bounds are easy to compute and can be estimated from a data set of zero-inflated random vectors as illustrated in this note with a motor insurance portfolio.

This paper deals with a retrial queuing system with a finite number of sources and collision of the customers, where the server is subject to random breakdowns and repairs depending on whether it is idle or busy. A significant difference of this system from the previous ones is that the service time is assumed to follow a general distribution while the server’s lifetime and repair time is supposed

A Correction to this paper has been published: https://doi.org/10.1007/s11009-021-09873-7

A Correction to this paper has been published: https://doi.org/10.1007/s11009-021-09868-4

In this paper, we consider two coherent systems having shared components. We assume that in the two systems there are three different types of components; components of type one that just belong to the first system, components of type two that lie only in the second system and components of type three that are shared by the two systems. We use the concept of joint survival signature to assess the joint

In this paper, we propose a stochastic model of the conditional time series of the wind chill index. The model is based on the inverse distribution function method and on the normalization method for simulation of the non-Gaussian non-stationary random processes as well as on the method of conditional distributions for simulation of the conditional Gaussian processes. In the framework of the approach

We study the economic analysis of a single server Markovian queueing system with positive and negative customers and multiple working vacations. Both positive and negative customers arrive in the system according to a Poisson process. Upon arrival, positive customers acquire some system information and decide whether to join or to balk the system based on the acquired information and a linear cost-reward

We are interested here in a theoretical and practical approach for detecting atypical segments in a multi-state sequence. We prove in this article that the segmentation approach through an underlying constrained Hidden Markov Model (HMM) is equivalent to using the maximum scoring subsequence (also called local score), when the latter uses an appropriate rescaled scoring function. This equivalence allows

In this paper, we investigate the optimal dividend problem under Parisian ruin with affine penalty payments at Parisian ruin time. The underlying risk process is assumed to be a spectrally negative Lévy risk process. With the help of the dynamic programming principle, we prove that the value function associated to our optimal control problem is the smallest solution with certain characteristics to

This work introduces and compares approaches for estimating rare-event probabilities related to the number of edges in the random geometric graph on a Poisson point process. In the one-dimensional setting, we derive closed-form expressions for a variety of conditional probabilities related to the number of edges in the random geometric graph and develop conditional Monte Carlo algorithms for estimating

The article studies the running maxima \(Y_{m,j}=\max_{1 \le k \le m, 1 \le n \le j} X_{k,n} - a_{m,j}\) where {Xk,n,k ≥ 1,n ≥ 1} is a double array of φ-subgaussian random variables and {am,j,m ≥ 1,j ≥ 1} is a double array of constants. Asymptotics of the maxima of the double arrays of positive and negative parts of {Ym,j,m ≥ 1,j ≥ 1} are studied, when {Xk,n,k ≥ 1,n ≥ 1} have suitable “exponential-type”

A hybrid preventive maintenance policy for heterogeneous degrading items is discussed. It combines the classical age-replacement strategy, when a system is replaced either on failure or at the predetermined age, with replacement of the system when degradation reaches the predetermined level at some intermediate time. Items come from two subpopulations with different reliability characteristics. Non-homogeneous

We consider an extended form of the MX/M/c queue with two types of server groups: Static as well as dynamic (which turn on/off in a state-dependent manner) servers. The two server groups may have homogenous or non-homogenous service rates. The model is further extended to feature setup and delayed-off times, finite capacity, and k staffing levels. This class of queues is solved via the difference equations

Consider a compound renewal risk model, in which a single accident may cause more than one claim. Under the condition that the common distribution of the individual claims is second order subexponential, we establish a second order asymptotic formula for the infinite-time ruin probability. Compared with the traditional ones, our second order asymptotic result is more precise and effective, which can

It has been observed in real networks that the fraction of nodes P(k) with degree k satisfies the power-law P(k) ∝ k−γ for k > kmin > 0. However, the degree distribution of nodes in these networks before kmin varies slowly to the extent of being uniform as compared to the degree distribution after kmin. Most of the previous studies focus on the degree distribution after kmin and ignore the initial

In this paper, we investigate several random structures, namely two classes of random lobster trees (RLTs) and a class of random spider trees (RSTs). The first class of RLTs grow with a fixed probability, whereas those from the second class evolve in a dynamic manner underlying a flavor of semi-opposite reinforcement. For these two classes, we characterize the structure of the random graphs therein

This paper presents a link between unbalanced non-linear urn model (a two-colored urn model) and stochastic approximation theory. Findings of our study reveal a successful establishment of limit laws for the urn composition, obtained under a drawing rule reinforced by an \(\mathbb {R}_{+}\)-valued concave function and a non-balanced replacement matrix.

We propose a method based on the Fourier transform for numerically solving backward stochastic differential equations. Time discretization is applied to the forward equation of the state variable as well as the backward equation to yield a recursive system with terminal conditions. By assuming the integrability of the functions in the terminal conditions and applying truncation, the solutions of the

This paper investigates the asset-liability management problem for an ordinary robust insurance system between a reinsurer and an insurer under the Heston model with delay. The reinsurer, as the leader of the Stackelberg game, can price reinsurance premium and invest its wealth in a financial market that contains a risk-free asset and a risky asset whose price process is described by the Heston model

In this paper, relations between some kinds of cumulative entropies and moments of order statistics are established. By using some characterizations and the symmetry of a non-negative and absolutely continuous random variable X, lower and upper bounds for entropies are obtained and illustrative examples are given. By the relations with the moments of order statistics, a method is shown to compute an

A periodic-review insurance model is studied under the following assumptions. One-period insurance claims form a sequence of independent identically distributed nonnegative random variables with a finite mean. At the beginning of each period a quota δ of the company surplus is invested in a non-risky asset for m periods. Theoretical expressions for finite-time and ultimate ruin probabilities, in terms

The present work proposes a new stationary integer-valued bilinear time series model with dependent counting series. The model will enable one to tackle the presence of some correlation between underlying events. The various probabilistic and statistical properties of the model are discussed, unknown parameters are estimated by several methods. Moreover, the performance of the estimation methods is

We present competing risks models within a semi-Markov process framework via the semi-Markov phase-type distribution. We consider semi-Markov processes in continuous and discrete time with a finite number of transient states and a finite number of absorbing states. Each absorbing state represents a failure mode (in system reliability) or a cause of death of an individual (in survival analysis). This

This paper is interested in studying a type of production models-stocks that can be seen as a stochastic fluid flow system with upward jumps at level zero. The joint distribution of the stocks level and the controlling Markov process is governed by two differential systems with specific boundary conditions. The uniqueness of the solution of this problem has been proved. Also, a unified solution with

Okisaka et al. (2017) investigated the eigen-distribution for multi-branching trees weighted with (a,b) on correlated distributions, which is a weak version of Saks and Wigderson’s (1986) weighted trees. In the present work, we concentrate on the studies of eigen-distribution for multi-branching weighted trees on independent distributions. In particular, we generalize our previous results in Peng et

We introduce the random exponential recursive tree in which at each point of discrete time every node recruits a child (new leaf) with probability p, or fails to do so with probability 1 − p. We study the distribution of the size of these trees and the average level composition, often called the profile. We also study the size and profile of an exponential version of the plane-oriented recursive tree

In this paper, a jump-diffusion Omega model with a two-step premium rate and a threshold dividend strategy is studied. For this model, the surplus process is a perturbation of a compound Poisson process by a Brownian motion. Firstly, using the strong Markov property, the integro-differential equations for the expected discounted dividend payments function, the Gerber-Shiu expected discounted penalty

In this paper, delta and extreme shock models and a mixed shock model which combines delta-shock and extreme shock models are studied. In particular, the interarrival times between successive shocks are assumed to belong to a class of matrix-exponential distributions which is larger than the class of phase-type distributions. The Laplace -Stieltjes transforms of the systems’ lifetimes are obtained

The Markov renewal process (MRP) of M/G/1 type has been used for modeling many complex queueing systems with correlated arrivals and the special types of transitions of the MRP process corresponds to the departures from the queueing system. It can be seen from the central limit theorem for regenerative process that the distribution of the number of transitions of MRP is asymptotically normal. Thus

A matrix variate generalization of the two-sided power distribution is proposed. Several properties of this distribution including probability density function, cumulative distribution function and characteristic function are derived.

This paper presents several numerical applications of deep learning-based algorithms for discrete-time stochastic control problems in finite time horizon that have been introduced in Huré et al. (2018). Numerical and comparative tests using TensorFlow illustrate the performance of our different algorithms, namely control learning by performance iteration (algorithms NNcontPI and ClassifPI), control

We analyze a multi-processor two-stage tandem call center retrial queueing network in which the processors are subject to active breakdowns and repairs at stage-I. A level-dependent quasi-birth-and-death (LDQBD) process is formulated and a sufficient condition for ergodicity of the system is discussed. Under the stability condition, the stationary distribution of the number of calls in the system,

We consider batch size selection for a general class of multivariate batch means variance estimators, which are computationally viable for high-dimensional Markov chain Monte Carlo simulations. We derive the asymptotic mean squared error for this class of estimators. Further, we propose a parametric technique for estimating optimal batch sizes and discuss practical issues regarding the estimating process

A simple and complete solution to determine the distributions of queue lengths at different observation epochs for the model GIX/Geo/c/N is presented. In the past, various discrete-time queueing models, particularly the multi-server bulk-arrival queues with finite-buffer have been solved using complicated methods that lead to results in a non-explicit form. The purpose of this paper is to present a

Many hedge funds and retail investors demand volatility and variance derivatives in order to manage their exposure to volatility and volatility-of-volatility risk associated with their trading positions. The Heston model is a standard popular stochastic volatility model for pricing volatility and variance derivatives. However, it may fail to capture some important empirical features of the relevant

Poisson processes are widely used to model the occurrence of similar and independent events. However they turn out to be an inadequate tool to describe a sequence of (possibly differently) interacting events. Many phenomena can be modelled instead by Hawkes processes. In this paper we aim at quantifying how much a Hawkes process departs from a Poisson one with respect to different aspects, namely,

Association or interdependence of two stock prices is analyzed, and selection criteria for a suitable model developed in the present paper. The association is generated by stochastic correlation, given by a stochastic differential equation (SDE), creating interdependent Wiener processes. These, in turn, drive the SDEs in the Heston model for stock prices. To choose from possible stochastic correlation

In this article we investigate the performance of scan statistics based on moving medians, as test statistics for detecting a local change in population mean, for one and two dimensional normal data, in presence of outliers, when the population variance is unknown. For fixed window scan statistics, both the training sample and parametric bootstrap methods are employed for one and two dimensional normal

We propose a class of evolution models that involves an arbitrary exchangeable process as the breeding process and different selection schemes. In those models, a new genome is born according to the breeding process, and after that a genome is removed according to the selection scheme that involves fitness. Thus, the population size remains constant. The process evolves according to a Markov chain

The original version of this article contained mistakes, and the author would like to correct them.

Now is an opportune time to revisit Stein’s (1973) beautiful lemma all over again. It is especially so since researchers have recently begun discovering a great deal of potential of closely related Stein’s unbiased risk estimate (SURE) in a number of directions involving novel applications. In recognition of the importance of the topic of Stein’s (1973; Ann Statist 9:1135–1151, 1981) research and its

We present a new approach to study big data in finance (specifically, in limit order books), based on stochastic modelling of price changes associated with high-frequency and algorithmic trading. We introduce a big data in finance, namely, limit order books (LOB), and describes them by Lobster data-academic data for studying LOB. Numerical results, associated with Lobster and other data, are presented

In this paper we consider a single server queueing model with under general bulk service rule with infinite upper bound on the batch size which we call group clearance. The arrivals occur according to a batch Markovian point process and the services are generally distributed. The customers arriving after the service initiation cannot enter the ongoing service. The service time is independent on the

The Hartman-Watson distribution with density \(f_{r}(t)=\frac {1}{I_{0}(r)} \theta (r,t)\) with r > 0 is a probability distribution defined on \(t \in \mathbb {R}_{+}\), which appears in several problems of applied probability. The density of this distribution is given by an integral θ(r, t) which is difficult to evaluate numerically for small t → 0. Using saddle point methods, we obtain the first

It is well known that the empirical distribution function has superior properties as an estimator of the underlying distribution function F. However, considering its jump discontinuities, the estimator is limited when F is continuous. Mixtures of the binomial probabilities relying on Bernstein polynomials lead to good approximation properties for the resulting estimator of F. In this paper, we establish

A specific function f(r) involving a ratio of complicated gamma functions depending upon a real variable r(> 0) is handled. Details are explained regarding how this function f(r) appeared naturally for our investigation with regard to its behavior when r belongs to R+. We determine explicitly where this function attains its unique minimum. In doing so, quite unexpectedly the customary Cramér-Rao inequality

This paper analyzes an infinite-buffer single-server bulk-service queueing system in which customers arrive according to a discrete-time renewal process. The customers are served under the discrete-time Markovian service process according to the general bulk-service rule. The matrix-geometric method is used to obtain the queue-length distribution at prearrival epoch. The queue-length distributions